Esperanto has 3 verbs for try peni, klopodi, provi. I think I might favour peni or strebi.
Provi doesn't seem quite right here.' I try to give money to my parents' suggests a situation in which you do this if you can (eg if you have some left over after your own expenses).
This is different to trying to give money to your parents and finding them too proud to accept it. In that case you might use provi.
When I read the sentence, my thoughts were in the line of "too proud to accept it." It wasn't until I read your comment that I realized there was another interpretation.
Would "klopodi" fit better here? I understood "provi" to be more "put to the test", "sample", "take the measure of" etc. rather than "attempt to do".
"Provi" is the most common, most general, and broadest of the words used to indicate "attempt", in some sense. It also has other meanings, as you indicate. "Klopodi" is more specific, but they can both be used to express some very similar ideas. In this sentence, "klopodi" would give me a sense of greater effort or more impediments that "provi".